A factory manufactures steel scales with mean thickness 0.032 cm. A random sample of 10 scales was found to have mean thickness of 0.030 cm with a standard deviation of 0.002 cm. [t9(0.05) = 2.262].
A. $\bar{x}$ = 0.03 cm, $\mu$ = 0.032 cm
B. $\bar{x}$ = 0.032 cm, $\mu$ = 0.03 cm
C. $|t|=3$
D. Null hypothesis is rejected.
E. Alternative hypothesis is rejected.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → A, C, D only
$\bar{x}=0.030,\;\; \mu=0.032,\;\; s=0.002,\;\; n=10$
$t=\frac{\bar{x}-\mu}{s/\sqrt{n}}$
$=\frac{0.030-0.032}{0.002/\sqrt{10}}$
$=\frac{-0.002}{0.002/\sqrt{10}}=-\sqrt{10}\approx -3.16$
$|t|\approx 3$
$t_{0.05,9}=2.262$
$|t|>2.262 \Rightarrow \text{Reject } H_0$
Correct statements are A, C and D.